How to find discrete contact symmetries

Abstract

This paper describes a new algorithm for determining all discrete contact symmetries of any differential equation whose Lie contact symmetries are known. The method is constructive and is easy to use. It is based upon the observation that the adjoint action of any contact symmetry is an automorphism of the Lie algebra of generators of Lie contact symmetries. Consequently, all contact symmetries satisfy various compatibility conditions. These conditions enable the discrete symmetries to be found systematically, with little effort.

References in corpus (2)

• Conformal Symmetries of the Self-Dual Yang-Mills Equations
• On Infinite-Dimensional Algebras of Symmetries of the Self-Dual Yang-Mills Equations

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• The ADHM construction and non-local symmetries of the self-dual Yang-Mills equations
• Surprising symmetry properties and exact solutions of Kolmogorov backward equations with power diffusivity
• Hidden symmetries, hidden conservation laws and exact solutions of dispersionless Nyzhnyk equation